Corso: Linear Programming

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Linear Programming Open course

Minimizza tutto Espandi tutto
Contributors : Nadia Brauner (UGA, Grenoble), Hadrien Cambazard (Grenoble-INP), Nicolas Catusse (Grenoble-INP), Aurélie Lagoutte (UCA, Clermont), Pierre Lemaire (Grenoble-INP)
Contact : Nadia Brauner
- One idea, one story: He did not know it was impossible, so he did it Pagina
  
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- Course supports
- Vous devez être inscrit dans le cours pour avoir accès à l'éditeur des exercices de programmation (une fois connecté, si vous voyez encore ce message, utilisez la roue dentée en haut à droite).
LP modelling
- Short OPL Tutorial File
  
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- OPL User Guide 1: Modeling LP problems with OPL using Caseine editor File
  
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- Mode d'emploi d'une activité de modélisation File
  
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- Play with the example of the user guide Virtual programming lab
  
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- Sand Box Virtual programming lab
- Know the definitions associated to LP: feasible solution, optimal solution, feasible region…
  
  Know the elements that form an LP: decision variables, objective function, constraints
  
  Be able to model an LP from a simple problem described in natural language
- I read the course Quiz
  
  Ricevere una valutazione
- Self training (a modelling problem)
- Cucumbers and onions Virtual programming lab
  
  Ricevere una valutazione
- Usine chimique Virtual programming lab
  
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- German Wines Virtual programming lab
  
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- Perfumes Virtual programming lab
  
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- Advertizing Virtual programming lab
  
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- Dairy Products Virtual programming lab
  
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- Airline - Compagnie aérienne Virtual programming lab
  
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- Apples Virtual programming lab
  
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- The teapot - Le pot de terre et la théière Virtual programming lab
  
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- OPL User guide: Modeling LP problems with OPL with external data
- Production of wines with external data Virtual programming lab
  
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- Bill Of Materials Virtual programming lab
  
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LP solving
- One idea, one story: the simplex algorithm is in the top 10 Pagina
  
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- Recognize the canonical and standard forms and know the transformations
  
  Linearize an objective function of the form maximum of a minimum or minimum of a maximum
- Playing with forms Quiz
  
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- Forms step by step Quiz
- Solve graphically an LP with two variables:
  
  draw the feasible region
  
  draw the level lines for the objective function
  
  find the optimal solution(s) on the graphic
- Draw LPs in 2D with Geogebra
- Graphical representation of Cucumbers and onions with Geogebra
  
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- Towards a solution Quiz
  
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- Know the definition of a basis, a basic and a non-basic variable a basic solution and a feasible basic solution
  
  Make the connection between the graphical representation and the basic solutions (find the point corresponding to a basic solution and conversely)
  
  Know the relation between the extreme points of the feasible region and the feasible basic solutions
- Bases Quiz
  
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- Go further with bases ** Quiz
  
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- Know the notion of pivoting and neighbor basis
  
  Before pivoting, recognize the variable that can enter the basis in order to improve the current solution
  
  While pivoting, know which variable can leave the basis
  
  Master the pivoting algorithm and be able to interpret it graphically
- Interactive illustration of the simplex method Pagina
- I read the course again Quiz
  
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- Let's pivot Quiz
  
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- Phase I * Quiz
  
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- "software without mathware is only footware"
  Philosophe contemporain inconnu
  Go further with linear Programming
- A CPLEX Example Virtual programming lab
- A song to understand simplex method (based on the tableau method) URL
Duality ☯
- One idea, one story: the physics of shortest paths to detect useless streets ! Pagina
  
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- OPL User Guide: Analyse the value of the dual variables
- Write the dual of a linear program
  
  Calculate the units of the dual variables
  
  Give an economical interpretation of the dual variables
- 5 minutes pour apprendre à écrire le dual d'un programme linéaire (in French) URL
  
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- Vidéo (12min): Une façon de comprendre la construction du dual Pagina
- Dual program Virtual programming lab
  
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- Vitamins Virtual programming lab
  
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- Vitamins (Q2) Virtual programming lab
  
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- Cucumber and onions culture (again!) Virtual programming lab
  
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- Wines (Q1) Virtual programming lab
  
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- Wines (Q2) Virtual programming lab
  
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- Know the weak duality theorem and its application to make a proof of optimality
  
  Know the strong duality theorem and understand its interest
  
  Apply the complementary slackness property to find the values of the dual variables
  
  Describe an optimality proof for a given basis
- Le théorème des écarts complémentaires (in French) Lezione
  
  Raggiungere la fine dell'attività
- I read the Duality course Quiz
  
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- A transportation problem
- The primal Quiz
  
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- The dual Quiz
  
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- A lab for the primal Virtual programming lab
  
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- A lab for the dual Virtual programming lab
  
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- Dualité en théorie des jeux (in french) Lezione
  
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Sensitivity analysis
- Understand the relation between the dual variable and the shadow price
  
  Understand why the value of the dual variable does not change when the second member of the constraint is changed in the primal as long as the basis remains the same
  
  Understand the meaning of the complementary slackness property on the example
  
  Be able to calculate the validity bounds of the value of a dual variable
- Discover Exel Solver Pagina
  
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- Sensitivity Analysis Quiz
  
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- Sensitivity analysis training Quiz
  
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- Sensitivity analysis training (old, do not use) Quiz
  
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- A complete exercice Quiz
  
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Place for contributors
This section is dedicated to new contributions on linear programming. You can add ideas in the forum and activities or course documents below.
- Ideas and contributions for linear programming Forum
- Collections collaborative d'exercices de programmation linéaires Database

Indice degli argomenti

Linear Programming Open course

LP modelling

LP solving

Duality ☯

Sensitivity analysis

Place for contributors